Solve for $x$ : $6x^2 - 84x + 270 = 0$
Solution: Dividing both sides by $6$ gives: $ x^2 {-14}x + {45} = 0 $ The coefficient on the $x$ term is $-14$ and the constant term is $45$ , so we need to find two numbers that add up to $-14$ and multiply to $45$ The two numbers $-9$ and $-5$ satisfy both conditions: $ {-9} + {-5} = {-14} $ $ {-9} \times {-5} = {45} $ $(x {-9}) (x {-5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -9) (x -5) = 0$ $x - 9 = 0$ or $x - 5 = 0$ Thus, $x = 9$ and $x = 5$ are the solutions.